Multiple choice

In the given question, two equations, numbered I and II, are given. Solve both the equations to get the appropriate answer. I. 2x2 - 87x + 43 = 0 II. y2 - 2y - 63 = 0

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x = y or the relationship cannot be established

  5. If x ≤ y
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving 2x^2 - 87x + 43 = 0 gives x = 43 or 0.5. Solving y^2 - 2y - 63 = 0 gives y = 9 or -7. Comparing the sets {43, 0.5} and {9, -7}, the relationship cannot be established.

AI explanation

Factoring equation I gives x = (87 ± sqrt((-87)^2 - 4(2)(43))) / (2*2) = (87 ± sqrt(6809)) / 4. Since the square root of 6809 is roughly 82.5, the roots for x are approximately 1.12 and 42.37. Factoring equation II gives (y - 9)(y + 7) = 0, making the roots for y equal to 9 and -7. Because the larger x value is greater than both y values, but the smaller x value falls between the two y values, no distinct relationship can be established.

Keep practicing — related questions